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- Evaluate the following initial value problem using the Laplace transform and the partial fraction decompositionDetermine the inverse laplace using partial fraction, show complete solutions and provide the checking. 2. F(s)= -3S+1/S²+6S+8To find the inverse transforms, first express the given function of s into partial fractions which will, then be recognizable as one of the following standard form: 1. L-1[1/(s2-a2)] = (1/a) sinh at 2. L-1[s/(s2-a2)] = cosh at